Question

A bridge is supported by triangular braces. If the sides of each brace have lengths 63 feet, 46 feet, and 40 feet, find the measure of the angle opposite the 46 foot side. Round to the nearest degree.

Answer 1

Given:

The sides of each brace have lengths 63 feet, 46 feet, and 40 feet.

To find:

The measure of the angle opposite the 46 foot side.

Solution:

According to the Law of Cosines:

`\cos A=(b^2+c^2-a^2)/(2bc)`

We need to find the measure of the angle opposite the 46 foot side. So,
`a=46` and the other sides are
`b=63,c=40`.

`\cos A=((63)^2+(40)^2-(46)^2)/(2(63)(40))`

`\cos A=(3969 +1600-2116)/(5040)`

`\cos A=(3453)/(5040)`

`\cos A=(1151)/(1680)`

Taking cos inverse on both sides, we get

`A=\cos^(-1)(1151)/(1680)`

`A=46.75503`

`A\approx 47`

Therefore, the measure of the angle opposite the 46 foot side is 47 degrees.